Constraint Generation Research Articles

Optimization of renewable energy-based integrated energy systems: A three-stage stochastic robust model

The integration of renewable energy into an integrated energy system (REIES) represents a promising approach to achieving clean and low-carbon energy consumption. However, the inherent uncertainty and variability of renewable energy sources and load demands present significant challenges to the operational efficiency and stability of REIES. To address these challenges, we propose a three-stage stochastic robust optimization (TRSRO) model. This model accounts for market electricity prices, source-load scenario probabilities, and output uncertainties to optimize system configurations in REIES. It also includes the optimization of power exchanges with the regional grid and strategic operational scheduling. Initial scenarios of uncertainty variables are generated using the spectral normalized conditional Wasserstein generative adversarial network (SNCWGAN), forming polyhedral uncertainty sets. Comprehensive norm constraints are then applied to capture probability distribution uncertainties within these sets. To improve the efficiency of solving the model, we introduce a two-layer column constraint generation algorithm, considering variable alternate iterations (TLCCG-VAI). The results demonstrate that the proposed method can achieve a 12.16 % reduction in total cost compared to the baseline method. Furthermore, the TLCCG-VAI algorithm reduces runtime by 82.97 % while maintaining the same level of solution accuracy.

Type Inference Logics

Type inference is essential for statically-typed languages such as OCaml and Haskell. It can be decomposed into two (possibly interleaved) phases: a generator converts programs to constraints; a solver decides whether a constraint is satisfiable. Elaboration, the task of decorating a program with explicit type annotations, can also be structured in this way. Unfortunately, most machine-checked implementations of type inference do not follow this phase-separated, constraint-based approach. Those that do are rarely executable, lack effectful abstractions, and do not include elaboration. To close the gap between common practice in real-world implementations and mechanizations inside proof assistants, we propose an approach that enables modular reasoning about monadic constraint generation in the presence of elaboration. Our approach includes a domain-specific base logic for reasoning about metavariables and a program logic that allows us to reason abstractly about the meaning of constraints. To evaluate it, we report on a machine-checked implementation of our techniques inside the Coq proof assistant. As a case study, we verify both soundness and completeness for three elaborating type inferencers for the simply typed lambda calculus with Booleans. Our results are the first demonstration that type inference algorithms can be verified in the same form as they are implemented in practice: in an imperative style, modularly decomposed into constraint generation and solving, and delivering elaborated terms to the remainder of the compiler chain.

Two-stage robust optimization for optimal operation of hybrid hydrogen–electricity storage system considering ladder-type carbon trading

The prominent problems of renewable energy curtailment and its uncertainty have become a hot topic. To the end, with consideration of environmental friendliness, energy utilization efficiency and operation cost, this paper proposes a hybrid hydrogen–electricity storage system (HHES) operation framework comprising assorted types of coupling devices and carbon capture system (CCS) under ladder-type carbon trading (LCT) mechanism. By considering energy balance constraints, equipments’ operation constraints and erratic rates of RESs and multiple loads, a scheduling model with source-load uncertainties is developed with the goal of minimizing the system’s operation cost and carbon emission. Then, a two-stage tri-level robust model is built to find the optimal scheduling plan under multiple uncertainties given the various sources and loads. The first level is to make an optimal dispatch plan and the second level is to find the worst scenario under the given uncertainty set. The third level aims at enhancing renewable energy accommodation rate and reducing load shedding rate in the worst case. Since the model is formed as a tri-level mixed integer optimization problem, the Column and Constraint Generation (CCG) method is adopted to achieve the optimal result. Finally, numerical analyses are performed. The results show that the proposed approach realizes a flexible dispatch of multiple energy and a high utilization level of multiple storages. Furthermore, this paper studies the influence of uncertainty and uncertainty budget parameters with the comparison of the deterministic model and robust models with different uncertainties. The results show that the proposed HHES has strong robustness and can provide a good reference for energy dispatch.

Bio-mimicking DNA fingerprint profiling for HLS watermarking to counter hardware IP piracy

The multifaceted, multivendor-based global design supply chain induces hardware threats of intellectual property (IP) piracy for modern computing and electronic systems. Current hardware watermarking techniques fall short either in terms of watermark strength (size of covert constraints generated) or number of security layers/variables involved in the security constraints generation process. This paper presents a novel approach for high level synthesis (HLS) watermarking by bio-mimicking DNA fingerprint profiling to counter hardware IP piracy. The proposed approach effectively captures the vital DNA fingerprint profiling phases such as DNA sequencing, DNA fragmentation, fragment replication, DNA ligase, etc. and bio-mimics them to generate a digital watermarking framework. The presented approach has been demonstrated on convolutional layer and JPEG compression-decompression (CODEC) algorithms that are widely used in several medical and machine learning applications. The proposed approach has been thoroughly compared with several state-of-the-art approaches. The proposed approach depicts superior security in the probability of coincidence of up to ~ 104 and tamper tolerance of up to ~ 10368 at 0% overhead as compared to the prior approaches.

Proactive Prevention Strategies for Grid Risk Scenarios Based on Pumped Storage Participation

Given the increasing importance of cascading trip prevention, this study presents the pumped storage characteristics to cooperate with thermal units and further ensure the safety of grid operation. The proposed model comprises two phases: the first phase is the day-ahead decision-making phase, which synergistically optimizes thermal units and pumped storage to improve the flexibility of grid operation; the second phase is the intra-day adjustment phase considering the uncertainty of the wind-photovoltaic and transmission line failure outage to enhance the robustness. Furthermore, this model employs a column and constraint generation algorithm to solve the two-phase, three-layer optimization problem, thereby minimizing the adjustment cost under the riskiest scenarios. The experimental results show that adding pumped storage reduces the total system operating cost by 3.99%, the renewable energy abandonment rate to 0.65%, and the thermal power unit output standard deviation to 74.13 MW.

Integration of the wind and solar power for the dynamic economic emission dispatch with the charging and discharging of plug-in electric vehicles

Wind and solar power are incorporated into the dynamic economic emission dispatch with the plug-in electric vehicles (DEED-PEV) in this paper, seeking to reduce the generation cost and pollutant emission significantly. A Laplacian non-dominated sorting genetic algorithm-II (LNSGA-II) and a constraint handling method (CHM) are proposed for the DEED-PEV. The LNSGA-II applies the Laplace distribution to both the crossover and mutation. The Laplace-based crossover makes each individual carry out unidirectional search towards its partner and enhances the information exchange between each pair of individuals. The Laplace-based mutation makes each individual carry out bi-directional search surrounding itself and adjust the searching range adaptively. Therefore, the LNSGA-II is able to explore and exploit the decision space of the DEED-PEV sufficiently, contributing to the reductions of the generation cost and pollutant emission in the objective space. For the variables of every individual, the CHM limits them within the feasible operating zones. The CHM also limits them within the dynamic boundaries. It further adjusts them according to the power balances. The power generation constraints and up/down ramp rate constraints can be always satisfied while the elimination of the total violation of the other constraints can be expedited. Therefore, the CHM can transform infeasible individuals to feasible ones rapidly. Four strategies are investigated for six PEV charging/discharging scenarios. The first three strategies consider no more than one kind of renewable energy generation while the fourth strategy involves both the wind power and solar power. Experimental results suggest that the fourth strategy is more economical and environment-friendly than the other three strategies. Furthermore, the LNSGA-II outperforms the other three competitor algorithms for six DEED-PEV problems in the light of hypervolume, coverage rate and spacing.

An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints

An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints

The Robust Optimization of Low-Carbon Economic Dispatching for Regional Integrated Energy Systems Considering Wind and Solar Uncertainty

In this paper, a two-stage robust optimization approach is employed to address the variability in renewable energy output by accounting for the uncertainties associated with wind and solar energy. The model aims to achieve a balanced system that is both low-carbon and economically efficient while also being resilient to uncertainties. Initially, a regional integrated energy system model is developed, integrating electricity, gas, and heat. The variability of wind and photovoltaic power outputs is represented using a modifiable uncertainty set. A resilient optimal scheduling model is formulated in two stages, with the objective of minimizing costs under worst-case scenarios. This model is solved iteratively through a column and constraint generation approach. Additionally, the scheduling model incorporates horizontal time shifts and vertical complementary substitutions for carbon trading costs and demand-side loads to avoid excessive conservatism and to manage carbon emissions and energy trading in the regional integrated energy system (RIES). Results show that the two-stage robust optimization approach significantly enhances the system’s resilience to risks and minimizes economic losses. The inclusion of carbon trading mechanisms and the demand response prevents the system from becoming overly robust, which could impede economic growth, while also reducing carbon emissions. The proposed method effectively achieves balanced optimal scheduling for a robust, economical, and low-carbon system.

Global supply chain flow planning for Chinese manufacturing under the BRI: An SFG-DRO method

The Belt and Road Initiative (BRI) has fostered the free flow of commodities and optimal distribution of resources for the global manufacturing supply chain (GMSC), meanwhile confronted with risks and uncertainties. This paper proposes the SFG-DRO method, which can well solve the flow distribution problem of GMSC under the BRI with uncertainties. The proposed method combines trend prediction from the stochastic frontier gravity (SFG) model with 1-Wasserstein fuzzy set-based distributionally robust optimization (DRO). Additionally, this paper integrates the principles of the column and constraint generation (C&CG) algorithm with the particle swarm optimization (PSO) algorithm to handle the above two-stage nonlinear problems efficiently. The results show that the SFG-DRO distribution method significantly reduces transportation costs by 25% and enhances security. By examining flow distribution across three key BRI channels, this paper identifies underexploited markets along the southward channel and substantial market potential with security risks along the northeast sea-land channel, proposing relevant improvement suggestions.

A Neural Network Approach to Physical Information Embedding for Optimal Power Flow

With the increasing share of renewable energy in the power system, traditional power flow calculation methods are facing challenges of complexity and efficiency. To address these issues, this paper proposes a new framework for AC optimal power flow analysis based on a physics-informed convolutional neural network (PICNN) approach, which enables the neural network to learn solutions that follow physical laws by embedding the power flow equations and other physical constraints into the loss function of the network. Compared with the traditional power flow calculation method, the calculation speed of this method is improved by 10–30 times. Compared to traditional neural network models, the method provides higher accuracy, with an average increase in accuracy of up to 2.5–10 times. In addition, this paper introduces a methodology to extract worst-case guarantees for violations of the neural network’s predicted power generation constraints, determining the worst possible violation that could result from any neural network output across the entire input domain, and taking appropriate measures to reduce the violation. The method is experimentally shown to be highly accurate and reliable for the AC optimal power flow (AC-OPF) analysis problem, while reducing the dependence on a large amount of labelled data.

An assessment methodology for the flexibility capacity of new power system based on two-stage robust optimization

The inherent variability in wind and solar power output presents a significant challenge to the flexibility balance of power systems. This paper introduces an innovative method for evaluating the flexibility capacity of a new power system, employing a two-stage robust optimization approach. Firstly, a power system flexibility supply and demand balance mechanism model is constructed and quantitatively characterized for the power system flexibility shortfalls set. Subsequently, taking into account timescale characteristics and directionality, the time series production simulation technique is applied to establish the effective ramping and flexibility supply distribution model of thermal power and energy storage units, enabling an analysis of the power system's supply regulation capabilities. On this basis, a power system flexibility capacity assessment method is proposed, which divides the system regulation resources into demand set and supply set, and constructs a power system flexibility capacity assessment model to ensure that the maximum system flexibility margin and the lowest operating cost are taken as the optimization objectives under the system security operation constraints. The column and constraint generation (C&CG) robust optimization algorithm is used to decompose the master problem and the max-min dual-layer subproblems for iterative solving, and the optimal capacity of each unit of the system in terms of output and flexibility is derived. Finally, the effectiveness and superiority of the proposed method is verified through case analysis, which shows that the method can improve the flexibility capacity by 14.9% and reduce the operating cost by 15.83% compared with the traditional proportional allocation method.

MMD-DRO based economic dispatching considering flexible reserve provision from concentrated solar power plant

To achieve real-time power balance between uncertain resource and demand consumptions in locally standalone power systems with a high penetration of new energy, it is promising to build concentrated solar power (CSP) plants through the establishment of power generation and flexible reserve provision. To address that, a refined maximum mean discrepancy-distributionally robust optimization (MMD-DRO) based economic dispatching model considering flexible reserve provision from CSP plants is designed in this work. Remarkably, a maximum mean discrepancy (MMD)-based ambiguity set representing new energy uncertain outputs is carried out. This proposed MMD-based ambiguity set mathematically keeps the shape of an ellipsoid through kernel mean embedding and related reformulation, and its center is equivalated as a group of empirical distributions extracted from historical data. On this basis, the impact of CSP and relevant flexible reserve capabilities in combination with conventional thermal power units is analyzed, and the joint up-forward/down-forward reserve provision produced from thermal power units and CSP is derived. Furthermore, a two-stage economic dispatching model considering flexible reserve configurations is constructed, which can be solved by the column & constraint generation algorithm. Some results on a modified IEEE 30-bus test system have demonstrated the effectiveness of the proposed model.

Optimizing integrated berth allocation and quay crane assignment: A distributionally robust approach

In this research, we have formulated a Two-Stage Distributionally Robust Optimization (TDRO) model within the context of a mean–variance ambiguity set, specifically designed to address the challenges in the Integrated Berth Allocation and Quay Crane Assignment Problem (BACAP). A key consideration in this study is the inherent uncertainty associated with ships’ arrival times. During the initial stage, we derive a baseline schedule governing berth allocation and quay crane assignment. Anticipating potential disruptions arising from uncertain arrival delays, the second stage is meticulously formulated to determine the worst-case expectation of adjustment costs within the mean–variance ambiguity set. Subsequently, we undertake an equivalent transformation, converting the general TDRO model into a Two-Stage Robust Second-Order Cone Programming (TRO-SOCP) model. This transformation facilitates the application of the Column and Constraint Generation (C&CG) algorithm, ensuring the derivation of an exact solution. To address the computational intricacies associated with second-order cone programming, we propose two enhancement strategies for upper and lower bounds, aimed at expediting the solution process. Additionally, to contend with large-scale instances, we introduce a refinement and approximation method, transforming the TDRO model into a Mixed-Integer Programming (MIP) model. Furthermore, extensive numerical experiments are executed on both synthetic and real-life instances to validate the superior performance of our model and algorithms. In terms of the total cost, the TDRO model demonstrates superior performance compared with Two-Stage Stochastic Programming (TSP) and Two-Stage Robust Optimization (TRO) models.

A data augmentation method for multiaxial fatigue life prediction based on physics-informed tabular generative adversarial network

Abstract Currently, in the multiaxial fatigue life prediction problem, machine learning (ML) algorithms are still limited by small samples. For ML tasks requiring large amounts of data, this paper proposes a Conditional Tabular Generative Adversarial Network (CTGAN) model using a physical equation as a generation constraint. The proposed method can make synthetic samples satisfy specific physical knowledge. The method is evaluated using two datasets of different materials. ML-based algorithms verify the feasibility of using synthetic datasets for life prediction. Verification analysis shows that the proposed method successfully synthesizes high-quality multiaxial fatigue datasets and effectively improves the prediction accuracy of ML algorithms.

Research on data-driven, multi-component distribution network attack planning methods

As the physical power information system undergoes continual advancement, mobile energy storage has become a pivotal component in the planning and orchestration of multi-component distribution networks. Furthermore, the evolution and enhancement of big data technologies have significantly contributed to enhancing the rationality and efficacy of various distribution network planning and layout approaches. At the same time, multi-distribution networks have also confronted numerous network attacks with increasing probability and severity. In this study, a Petri net is initially employed as a modeling technique to delineate the network attack flow within the distribution network. Subsequently, the data from prior network attacks are consolidated and scrutinized to evaluate the vulnerability of the cyber-physical system (CPS), thereby identifying the most critical network attack pattern for a multi-component distribution network. Following this, the defender–attacker–defender planning methodology is applied for scale modeling, incorporating rapidly evolving mobile energy storage into the pre-layout, aiming to mitigate the detrimental impact of network attacks on the power grid. Ultimately, the column and constraint generation (C&CG) algorithm is utilized to simulate and validate the proposed planning strategy in a 33-node system with multiple control groups established to demonstrate the viability and merits of the proposed strategy.

Optimal robust sizing of distributed energy storage considering power quality management

AbstractThis paper proposes an optimal robust sizing model for distributed energy storage systems (DESSs) considering power quality management. The power conversion systems (PCSs) of DESSs with four‐quadrant operation characteristics can provide power quality management services to customers. To improve capacity utilization of the DESS, power quality management services are quantified and integrated into an optimal bi‐level sizing model, where the upper level addresses the sizing problem concerning battery and PCS capacities, while the lower level focuses on coordinating active/reactive power control of the DESS. A robust optimization approach for DESS scheduling is adopted to consider uncertainties of distributed photovoltaic (PV) power generation and power quality management requirements. The column and constraint generation (C&CG) algorithm is applied for efficient handling of this model. Ultimately, the effectiveness of the proposed approach is validated through comprehensive comparative analysis of four cases, resulting in a 12.44% increase in the net present value (NPV) over the entire lifecycle.

Low‐carbon economic operation of multi‐energy microgrid based on multi‐level robust optimisation

AbstractThe economic and low‐carbon operation strategy of multi‐energy microgrids (MEM) has become an important research topic in smart grids. The operation of MEM is affected by uncertain factors from renewable energy and internal load. To handle uncertainties from both source and load sides, the authors propose a novel worst‐case‐and‐probability uncertainty sets and a novel worst‐expectation min‐max‐max‐min two‐stage four‐level robust optimisation (RO) model considering stepped carbon trading for MEM. This four‐level RO model is a more generalised model compared with the traditional two‐stage RO and distributionally robust optimisation based models. First, the unsolvable original four‐level model is decoupled into a master problem and a sub‐problem (SP). Second, Karush–Kuhn–Tucker condition is applied to convert SP into a solvable problem. Third, column and constraint generation (C&CG) algorithm is employed to solve the reformulated four‐level RO. Finally, the effectiveness of the proposed model and solution method is verified by case studies. The results indicate that the convergence behaviour of this solution method is excellent. The MEM operator can select appropriate robustness factors and comprehensive norms to control its conservatism level. Besides, MEM could reduce carbon emissions by participating in carbon trading and installing carbon capture devices.

A multi-ship power sharing strategy: Using two-stage robust optimization and Shapley value approach

In recent years, the use of cold ironing (CI) has effectively reduced the carbon emissions of ships in port areas. However, due to the limitation of port CI quantity and power supply capacity, the power demand of some ships cannot be met. To solve this problem, this paper proposes a multi-ship power sharing strategy based on two-stage robust optimization and improved Shapley value method. Firstly, considering the uncertainty of ship photovoltaic power generation, a multi-ship power sharing model based on two-stage robust optimization is established. This model is a three-level optimization model with mixed integer variables, which is a NP-hard problem. In this paper, the nested column-and-constraint generation algorithm combined with duality theory and big-M method is used to obtain the optimal scheduling strategy of ship shared power, CI power and load demand response power. Secondly, an improved Shapley value method considering berth and remaining berthing time is proposed to realize the cost allocation in the process of ship power sharing. Finally, the effectiveness of the multi-ship power sharing strategy in reducing berthing costs and carbon emissions is verified by simulation. This method is expected to provide a new idea for the development of green ports.

Distributionally robust planning for power distribution network considering multi-energy station enabled integrated demand response

—To copy with the peak valley difference and peak load problem of power distribution network (PDN), this paper proposes a distributionally robust planning model for PDN considering the flexible management via the multi-energy station (MES) based integrated demand response (IDR). The planning covers reinforcement of the existing substation and feeders as well as the investment of MES and IDR. The IDR involves the incentive interruptible load response (ILR), transferable load response (TLR) and price-based power-gas substitution (PGS) which is implemented on MES. The MES integrates multiple energy storages and energy coupling devices, which is served as a platform for PDN operator to centrally track the final demand and improve the response potential of IDR. The proposed planning method aims at minimizing the present value of PDN investment cost and operation cost during the planning period. To handle the uncertainty of PDN end-use loads, a two-stage Kullback–Leibler divergence (KLD)-based distributionally robust optimization (DRO) planning model is formulated. Finally, the columns and constraints generation algorithm is utilized to solve the KLD-DRO planning model. Case studies are carried out on a practical 152-bus urban distribution system to validate the effectiveness of the proposed methodology and quantitatively analyze the key influence factors of PDN investment.

A novel improved harbor seal whiskers algorithm for solving hybrid dynamic economic environmental dispatch considering uncertainty of renewable energy generation

The originality of this work is introducing a novel Improved Harbor Seal Whiskers Algorithm (IHSWA) as an innovative and improved optimizer for solving complex hybrid dynamic economic-environmental dispatch (HDEED) considering uncertainty of renewable energy generation (REG) and various system constraints. IHSWA is implemented by hybridizing opposition-based algorithm (OBA) and local search algorithm (LSA) approaches to enhance the algorithm's search efficiency and overcome the challenges of other counterpart approaches. IHSWA has an optimal balancing feature between searching modes (exploring and exploiting modes). This feature makes the proposed algorithms more advanced than their counterpart optimizing techniques. The HDEED is modeled using a non-convex and non-smooth objective function, considering various equality and inequality constraints such as ramp rate bounds (RRLs), valve-point effects (VPE), production limits (PL), spinning reserves (SRLs), prohibited operating zones (POZs), and power balance (PB). The proposed approach is verified on a hybrid modified IEEE 57-bus 7-unit power system incorporating solar and wind energy generation. The proposed approach is compared with various modern optimization techniques, such as the traditional Harbor Seal Whiskers Algorithm (HSWA), the Lemurs Optimization Algorithm (LOA), the Nutcracker Optimization Algorithm (NOA), and the Artificial Hummingbird Algorithm (AHA). The incorporation of REG sources produces a significant reduction in operative costs and a remarkable decline in emissions. The convergence rate of the proposed approach indicates that the novel hybrid algorithm converges rapidly towards the optimal solution, achieving the best global optimum solution. The ANOVA test and the Tukey test are used to analyze the results statistically. The IHSWA approach shows superior advanced features with a best fuel cost of 1640.5890 $ and a minimum std. value of 1708.4895. While for emission objective minimizing, IHSWA attained a minimum emission cost and std. value of 1080.1629 kg and 1777.0770, respectively. The statistical analysis of the results approves the stability, reliability, and consistency of the proposed strategy with significant convergence. The appreciated contribution of this work is introducing a novel hybrid approach for solving HDEED efficiently, incorporating REG, and considering various system constraints. IHSWA has advanced features over its counterpart approaches. The contribution holds specific importance for the economic development of countries. It creates the path for increased self-sufficiency by reducing their need for fossil fuels for energy production. The study emphasizes the transition from being reliant on fossil fuels to the development of sustainable urban economies.